Related papers: A note on the voting problem

An election over a finite set of candidates is called single-crossing if, as we sweep through the list of voters from left to right, the relative order of every pair of candidates changes at most once. Such elections have many attractive…

We examine the following voting situation. A committee of $k$ people is to be formed from a pool of n candidates. The voters selecting the committee will submit a list of $j$ candidates that they would prefer to be on the committee. We…

A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper…

When voter preferences are known in an incomplete (partial) manner, winner determination is commonly treated as the identification of the necessary and possible winners; these are the candidates who win in all completions or at least one…

Usually a voting rule requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial…

We discuss voting scenarios in which the set of voters (agents) and the set of alternatives are the same; that is, voters select a single representative from among themselves. Such a scenario happens, for instance, when a committee selects…

An election is a pair $(C,V)$ of candidates and voters. Each vote is a ranking (permutation) of the candidates. An election is $d$-Euclidean if there is an embedding of both candidates and voters into $\mathbb{R}^d$ such that voter $v$…

The proportional veto principle, which captures the idea that a candidate vetoed by a large group of voters should not be chosen, has been studied for ranked ballots in single-winner voting. We introduce a version of this principle for…

For a voting ensemble that selects an odd-sized subset of the ensemble classifiers at random for each example, applies them to the example, and returns the majority vote, we show that any number of voters may minimize the error rate over an…

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…

Let p(n, k) denote the number of partitions of n into parts less than or equal to k. We show several properties of this function modulo 2. First, we prove that for fixed positive integers k and m, p(n,k) is periodic modulo m. Using this, we…

A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they…

May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to…

In many practical scenarios, a population is divided into disjoint groups for better administration, e.g., electorates into political districts, employees into departments, students into school districts, and so on. However, grouping people…

Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…

We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its…

An important question in elections is the determine whether a candidate can be a winner when some votes are absent. We study this determining winner with the absent votes (WAV) problem when the votes are top-truncated. We show that the WAV…

Ranked choice voting is vulnerable to monotonicity failure - a voting failure where a candidate is cost an election due to losing voter preference or granted an election due to gaining voter preference. Despite increasing use of ranked…

In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins…

In some preference aggregation scenarios, voters' preferences are highly structured: e.g., the set of candidates may have one-dimensional structure (so that voters' preferences are single-peaked) or be described by a binary decision tree…